19683/16384: Difference between revisions

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m Changed "classic major third" to classic minor third for 6/5 approximation
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{{Infobox Interval
{{Infobox Interval
| Name = Pythagorean augmented second
| Name = Pythagorean augmented second, Evadairean comma
| Color name = lw2, Lawa 2nd
| Color name = Lw2, lawa 2nd
}}
}}


The '''Pythagorean augmented 2nd''', '''19683/16384''', may be reached by stacking 9 3/2's and octave reducing. It differs from the classic minor third, [[6/5]], by the [[schisma]], and, as a result, the Pythagorean augmented second is in fact rather consonant. According to [[User:Aura|Aura]], while 19683/16384 may take the place of the classic minor third in chords, its status as a augmented second means that it has a different function in terms of voice-leading. If it is tempered out, you set the fifth to 5/9 and divide the octave into 9 parts, although only 9edo does this in it's patent val. If it is used as a generator, it produces [[Hanson]].
The '''Pythagorean augmented second''', '''19683/16384''', may be reached by stacking 9 3/2's and octave reducing. It differs from the classic minor third, [[6/5]], by the [[schisma]], and, as a result, the Pythagorean augmented second is in fact rather consonant and some may consider it a minor third (see [[Interval region]]).
 
== Temperaments ==
When this ratio is taken as a comma to be tempered out, it produces the [[tervenna]] temperament, and has been named the '''Evadairean comma''' (by analogy with the Pythagorean comma not sharing its name with compton temperament)<!-- who is Evadairean? -->. Edos tempering it out include [[9edo]], as well as [[18edo]] if its flat fifth is used. It can be used as a generator for [[hanson]].


== See also ==
== See also ==
* [[32768/19683]] – its [[octave complement]]
* [[8192/6561]] – its [[fifth complement]]
* [[8192/6561]] – its [[fifth complement]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
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[[Category:Second]]
[[Category:Second]]
[[Category:Augmented Second]]
[[Category:Augmented second]]
[[Category:Third]]
[[Category:Third]]
[[Category:Minor third]]
[[Category:Minor third]]

Latest revision as of 11:52, 27 September 2025

Interval information
Ratio 19683/16384
Factorization 2-14 × 39
Monzo [-14 9
Size in cents 317.595¢
Names Pythagorean augmented second,
Evadairean comma
Color name Lw2, lawa 2nd
FJS name [math]\displaystyle{ \text{A2} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 28.2647
Weil norm (log2 max(n, d)) 28.5293
Wilson norm (sopfr(nd)) 55
Open this interval in xen-calc

The Pythagorean augmented second, 19683/16384, may be reached by stacking 9 3/2's and octave reducing. It differs from the classic minor third, 6/5, by the schisma, and, as a result, the Pythagorean augmented second is in fact rather consonant and some may consider it a minor third (see Interval region).

Temperaments

When this ratio is taken as a comma to be tempered out, it produces the tervenna temperament, and has been named the Evadairean comma (by analogy with the Pythagorean comma not sharing its name with compton temperament). Edos tempering it out include 9edo, as well as 18edo if its flat fifth is used. It can be used as a generator for hanson.

See also